By Werner Müller
The manifolds investigated during this monograph are generalizations of (XX)-rank one in the neighborhood symmetric areas. within the first a part of the e-book the writer develops spectral concept for the differential Laplacian operator linked to the so-called generalized Dirac operators on manifolds with cusps of rank one. This contains the case of spinor Laplacians on (XX)-rank one in the community symmetric areas. The time-dependent method of scattering thought is taken to derive the most effects in regards to the spectral solution of those operators. the second one a part of the ebook offers with the derivation of an index formulation for generalized Dirac operators on manifolds with cusps of rank one. This index formulation is used to turn out a conjecture of Hirzebruch in regards to the relation of signature defects of cusps of Hilbert modular kinds and particular values of L-series. This booklet is meant for readers operating within the box of automorphic types and research on non-compact Riemannian manifolds, and assumes a data of PDE, scattering concept and harmonic research on semisimple Lie teams.
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